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Kolev, Nikolai

Discrete line integral on uniform grids: probabilistic interpretation and applications. (English) Zbl 1469.60060

Braz. J. Probab. Stat. 34, No. 4, 821-843 (2020).
Summary: Following the methodology developed by [J. M. Hyman and M. Shashkov, Comput. Math. Appl. 33, No. 4, 81–104 (1997; Zbl 0868.65006)], we define a discrete version of gradient vector and associated line integral along arbitrary path connecting two nodes of uniform grid. An exponential representation of joint survival function of bivariate discrete non-negative integer-valued random variables in terms of discrete line integral is established. We apply it to generate a discrete analogue of the Sibuya-type aging property, incorporating many classical and new bivariate discrete models. Several characterizations and closure properties of this class of bivariate discrete distributions are presented.

Cited in 1 Document

MSC:

60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions
39A12 Discrete version of topics in analysis
62N05 Reliability and life testing

Keywords:

bivariate geometric distributions; characterization; discrete bivariate lack of memory and aging properties; discrete gradient vector; failure rate; line integral; Marshall-Olkin model; reliability; Sibuya’s dependence function

Citations:

Zbl 0868.65006
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Full Text: DOI Euclid

References:

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